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"Professor Goddard does not know the relation between action and reaction and the need to have something better than a vacuum against which to react. He seems to lack the basic knowledge ladled out daily in high schools."
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Supplementary problems - Gravity
1. a) Determine the orbital speed of a satellite 160 km (About 100 miles) above the surface of the Earth. b) Determine the orbital speed of a satellite 100 km above the surface of the Earth. Do these answers suggest that NASA had to adjust the speed of the Apollo spacecraft as they traveled from here to there and back again?
2. a) Determine the speed of the Earth around the sun, given the radius of the Earth’s orbit and the length of the Earth year. b) Now use this speed and the equation you developed in problem #1 above to determine the mass of the sun. c) Articulate a scheme whereby one can know the mass of any central body by measuring the orbital radius and period of any satellite, and then applying those data as in 2b above.
3. Go to the astronomical data in References. Choose any two planets. For each planet calculate T squared/R cubed, where T is the orbital period about sun and R is the mean radius of the planetary orbit. What you have discovered here is Kepler’s law of periods.
4. Telstar was the first communications satellite launched in 1962. Because it was placed in near-Earth orbit, it had an orbital period of about 90 minutes and was therefore in a useful position for broadcasts toEurope for a few minutes every orbit. Syncom 2 was launched in 1963 and placed in geosynchronous orbit, meaning that it had an orbital period of 24 hours and appeared to hover over one spot over the equator. Use the equation that you derived in #1 above and the fact that v = 2 pi R/T (R = radius of orbit; T = period = 24 hours) to determine a) the orbit radius; and b) the orbit speed of a geosynchronous satellite.
5. Go to References to find astronomical data regarding the moon. Calculate the acceleration due to gravity on the moon if g = G M moon /(moon radius)*2.
6. Astrologers would have you believe that the position of the planets at the time of your birth had something to do with determining the outcome of your life. The equation g = G Mbody/(dist body to you)*2 gives you the gravitational field intensity (GFI) at some point in space. A) Calculate the GFI on the Earth caused by the planet Mars when Mars is closest to Earth. B) Now calculate the GFI of the obstetrician who delivered you at birth. Assume that he/she had a mass of 100 kg and was 1 m away from you. Which GFI is larger?
7. a) g on the surface of the Earth (which for our purposes is one Earth radius from the Earth) is close to 9.8 m/s/s. The moon is 60 RE from the Earth. At lunar mean distance g = (9.8 m/s/s) (1/60)*2 .Calculate this quantity in m/s/s. b) For an object moving in a circular path, a = (v*2)/R, where v = 2 pi R/T and R is the orbital radius of the moon and T is the period of the moon. Using values of R and T found in references, calculate the centripetal acceleration of the moon.
8. The formula describing the period of a pendulum is T = 2 pi (L/g)*1/2.where L is the length of the pendulum and g is the local acceleration due to gravity. (We will derive this equation in a few days.) Calculate the period for g = 9.800 m/s/s and again for 9.810 m/s/s/. Which clock keeps time slower than its mate. How long will it take before the slow clock loses one second.